US Senate Majority Leader Bill Frist said the Afghan guerrilla war can never be won militarily and called for efforts to bring the Taliban and their supporters into the Afghan government.
Frist said there are too many Taliban fighters with too much popular support to be defeated by military means.
"You need to bring them into a more transparent type of government," Frist said during a brief visit to a US and Romanian military base in the southern Taliban stronghold of Qalat.
"And if that's accomplished, we'll be successful," he added.
Frist said asking the Taliban to join the government was a decision to be made by Afghan President Hamid Karzai.
Senator Mel Martinez, a Republican accompanying Frist, said negotiating with the Taliban was not "out of the question," but added that fighters who refused to join the political process would have to be defeated.
"A political solution is how it's all going to be solved," he said.
In violence on Monday, a suicide bomber blew himself up next to a NATO convoy in Kabul, wounding three soldiers and three civilians, while a roadside bomb in the eastern Paktia Province killed three Afghan soldiers and wounded as many, officials said.
Afghanistan is being rocked by the worst outbreak of violence since the Taliban's ouster in late 2001. Militants are increasingly resorting to suicide attacks and roadside bombs.
Frist, who said he will announce in about a month if he plans to run for the US presidency, said he had hoped the US would soon be able to withdraw its forces from Afghanistan.
But the 20,000 US troops are still needed to help the 37-country coalition deal with an intensifying Taliban insurgency.
"We're going to need to stay here a long time," Frist said.
There appears to be an "unlimited flow" of Afghans and foreigners, he said, who are"willing to pick up arms and integrate themselves with the Taliban."
The only way to win in places like Qalat is to "assimilate people who call themselves Taliban into a larger, more representative government," he said.
"Approaching counterinsurgency by winning hearts and minds will ultimately be the answer," Frist said. "Military versus insurgency one-to-one doesn't sound like it can be won. It sounds to me ... that the Taliban [are] everywhere."
Three NATO troops suffered minor injuries in the suicide bombing in Kabul. Major Luke Knittig, a military spokesman, said he could not disclose the nationalities of the soldiers.
The attack came two days after another suicide bomber killed 12 people and wounded more than 40 outside Afghanistan's Interior Ministry.
In the southern province of Helmand, clashes on Sunday left 10 people dead, including five civilians, said Ghulam Muhiddin, the governor's spokesman.
The civilians were killed when their vehicle hit a freshly planted mine on a road usually used by NATO and Afghan security forces in Helmand's Musa Qala district, Muhiddin said.
A suspected Taliban on a motorbike, meanwhile, killed two policemen in Gereshk district, he said.
Separately, NATO-led troops killed three militants in Nawzad district.